Your choices are:
1) Reef Fishing - You'll be behind the reef with generally low seas, fishing for snapper (mostly yellow and red) and barracuda. You can anchor up or drift with bait on the bottom or you'll troll with spinners, spoons, jigs or bait.
2) Flats Fishing - You'll travel to the flats and attempt to fly fish. Certainly an acquired skill, you could ask for lessons but it aint that easy. You'll catch tarpon, permit and bonefish (or at least try). You will probably throw these fish back if you are able to get them aboard.
3) Deep Sea - You'll go outside the reef, either troll or drop bait. Must be a calm day and must be a bigger boat with lots of anchor line if you want to drop for bottom fish. You'll catch wahoo, sailfish, and possibly marlin while you troll and large grouper and snapper if you bait at the bottom.
Ask around the island for guides. The fishing options will vary with conditions. Stop by Anglers Abroad fly shop near the split, they know most of the guides on the island.